Download PDF by Duan Li Xiaoling Sun: Nonlinear Integer Programming (International Series in

By Duan Li Xiaoling Sun

ISBN-10: 0387295038

ISBN-13: 9780387295039

ISBN-10: 0387329951

ISBN-13: 9780387329956

A mix of either Integer Programming and Nonlinear Optimization, it is a strong booklet that surveys the sector and gives a cutting-edge therapy of Nonlinear Integer Programming. it's the first publication on hand at the topic. The booklet goals to deliver the theoretical starting place and resolution equipment for nonlinear integer programming to scholars and researchers in optimization, operations study, and laptop technological know-how.

Show description

Read Online or Download Nonlinear Integer Programming (International Series in Operations Research & Management Science) PDF

Similar linear programming books

Mathematical modelling of industrial processes: lectures by Stavros Busenberg, Bruno Forte, Hendrik K. Kuiken, Vincenzo PDF

The 1990 CIME path on Mathematical Modelling of commercial tactics set out to demonstrate a few advances in questions of commercial arithmetic, i. e. of the purposes of arithmetic (with all its "academic" rigour) to real-life difficulties. The papers describe the genesis of the types and illustrate their suitable mathematical features.

New PDF release: Primal-Dual Interior-Point Methods

There are primarily 2 well-developed useful equipment that dominate the answer tools identified for fixing linear programming (linear optimization) difficulties at the laptop. the 1st one is the "Simplex strategy" which used to be first built within the Forties yet has considering developed into an effective process by utilizing many algorithmic and reminiscence garage methods.

Read e-book online Controllability of partial differential equations governed PDF

The objective of this monograph is to deal with the difficulty of the worldwide controllability of partial differential equations within the context of multiplicative (or bilinear) controls, which input the version equations as coefficients. The mathematical types we research contain the linear and nonlinear parabolic and hyperbolic PDE's, the Schrödinger equation, and matched hybrid nonlinear allotted parameter platforms modeling the swimming phenomenon.

New PDF release: Fully Tuned Radial Basis Function Neural Networks for Flight

Absolutely Tuned Radial foundation functionality Neural Networks for Flight keep watch over offers using the Radial foundation functionality (RBF) neural networks for adaptive keep watch over of nonlinear structures with emphasis on flight keep an eye on functions. A Lyapunov synthesis technique is used to derive the tuning principles for the RBF controller parameters that allows you to warrantly the soundness of the closed loop process.

Additional resources for Nonlinear Integer Programming (International Series in Operations Research & Management Science)

Sample text

11. D If hj{x) > 0 for any x G X, j = 1 , . . 1 General case We consider the following unconstrained binary quadratic optimization problem: (BQ) min a:G{-l,l}"' q(x) = -x^Qx + b^x^ 2 Optimality, Relaxation and General Solution Procedures where Q is a symmetric matrix in R^^^ and 6 G M^. , n, can be transformed into the form of {BQ) by the Unear transformation: y^ — l^ + [m — li){xi + l)/2, i = 1 , . . , n. t. X;^^ — 1, Z = 1, . . , n . Problem {CQ) is essentially a nonconvex continuous optimization problem even if matrix Q is positive semidefinite.

So Az"" < b. Moreover, since c^d'^ = -XjAid^ < 0 for alH = 1 , , . 6) that c^^:* < c^z. 3), Moreover, combining c^2:* < c^z with the optimality of z and (2,4,6) leads to c^d'^ = 0 for z with /i^ > 1. 4,8) Then, Aix* = Aix - [fii\Aid^ [fit\Aid^ < Aix < b\ (2,4,9) Also, by (2,4,5), it holds X* - ^ + (/ii - [fli\)d^ + ... + (^^- [fit\)d\ Thus, we obtain ||x* — ^||oo < nA{A) using the similar arguments as in part (i). Moreover, we have A2X'' - A2Z + {in - [iii\)A2S + • • • + (/i^ - [iit\)A2d^ < A2Z < b^.

D Optimality, Relaxation and General Solution Procedures Notice that problem {BQ) is a box constrained convex quadratic programming problem and hence is much easier to solve than (BQ). Solving {BQ), however, in general only yields a real solution. The next result gives a sufficient condition for getting a nearby integer optimal solution to (BQ) based on a real optimal solution to (BQ). 15 Assume that Q is a real positive semidefinite matrix and X* is an optimal solution to {BQ). If z"" e. { — 1, l}'^ satisfies the following conditions: (i) zl = x^forxl e {-1,1}, and (ii) 2'*(5(2:* - X*) < Xmin{Q)e, where Z* = diag{z'') and \rnin{Q) is the minimum eigenvalue ofQ, then 2:* is an optimal solution to {BQ).

Download PDF sample

Nonlinear Integer Programming (International Series in Operations Research & Management Science) by Duan Li Xiaoling Sun


by William
4.5

Rated 4.32 of 5 – based on 15 votes